American Journal of Mathematical and Computational Sciences  
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Extension of the Method of Basic Trajectories by G. I. Marchuk for Modeling of Road Pavements via Laser Scanned Data
American Journal of Mathematical and Computational Sciences
Vol.3 , No. 3, Publication Date: Oct. 29, 2018, Page: 69-79
201 Views Since October 29, 2018, 42 Downloads Since Oct. 29, 2018

Boris Mihailovich Shumilov, Department of Applied Mathematics, Tomsk State University of Architecture and Building, Tomsk, Russia.


Andrey Nikolaevich Baigulov, JSC Indor-Most, Tomsk, Russia.


For polynomial splines of n-th degree with non-uniform knots the new type wavelet, semi-orthogonal according to scalar product with derivatives, is offered. With use of splitting on even and odd knots the algorithm of wavelet-decomposition via solution of band system of linear algebraic equations is received. The task of definition of factors of differential equations of nonlinear dynamic system is decided. For group of homogeneous objects of exponential type the equation of system is used in linearized form. The problems of modeling of surfaces of highways with use of data of laser scanning are described. The examples of imposing of the designed road pavement on the previously processed laser measurements are shown.


Non-Uniform Laser Measurements, Splines of Odd Degree, Multi-Scale Analysis, Wavelets, Differential Equations, Data Processing, Highways, Modeling


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